Verified answer

Derivada do quociente:

f(x) = a(x) / b(x)

f'(x) = [a'(x) . b(x) - a(x) . b'(x)] / [b(x)]²

............................................................................

f(x) = (x² + 1) / (x - 1)

f'(x) = [(x² + 1)' . (x - 1) - (x² + 1) . (x - 1)'] / (x - 1)²

f'(x) = [2x . (x - 1) - (x² + 1) . 1] / (x - 1)²

f'(x) = (2x² - 2x - x² - 1) / (x - 1)²

f'(x) = (x² - 2x - 1) / (x - 1)²

Ola Mezaque

f(x) = g(x)/h(x)

derivada de um quociente

(g/h)' ´= g'*h - g*h')/h²

g = x² + 1

g' = 2x

h = x - 1

h' = 1

f'(x) = (2x*(x - 1) - )x² + 1)*1))/x- 2)²

f'(x) = 2x² - 2x - x² - 1)/(x - 2)² = (x² - 2x - 1)/(x - 2)²

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